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# Realizability of Graph Specifications: Characterizations and Algorithms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11085)

## Abstract

The study of graphs and networks often involves studying various parameters of the graph vertices, capturing different aspects of the graph structure, such as the vertex degrees or the distances between the vertices. Given an n-vertex graph G and a parameter of interest f, one may associate with G a vector $$\mathcal{F}(G)=\langle f_1,\ldots ,f_n\rangle$$ giving the value of f for each vertex. This vector can be thought of as the f-profile of the graph. This paper concerns the dual problem, where given an n-entry f-specification vector $$F=\langle f_1,\ldots ,f_n\rangle$$, we need to decide whether it is possible to find a graph G realizing this specification, namely, whose f-profile $$\mathcal{F}(G)$$ conforms to $$F$$. The paper introduces the notion of graph realiziations and illustrates a number of example problems related to finding graph realiziations for given specifications.

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## Copyright information

© Springer Nature Switzerland AG 2018

## Authors and Affiliations

• Amotz Bar-Noy
• 1
• Keerti Choudhary
• 2
• David Peleg
• 2
• Dror Rawitz
• 3
Email author
1. 1.City University of New York (CUNY)New YorkUSA
2. 2.Weizmann Institute of ScienceRehovotIsrael
3. 3.Bar Ilan UniversityRamat-GanIsrael